Social Graph Ranker

1---2name: social-graph-ranker3description: Weighted social-graph ranking for warm intro discovery, bridge scoring, and network gap analysis across X and LinkedIn. Use when the user wants the reusable graph-ranking engine itself, not the broader outreach or network-maintenance workflow layered on top of it.4origin: ECC5---6 7# Social Graph Ranker8 9Canonical weighted graph-ranking layer for network-aware outreach.10 11Use this when the user needs to:12 13- rank existing mutuals or connections by intro value14- map warm paths to a target list15- measure bridge value across first- and second-order connections16- decide which targets deserve warm intros versus direct cold outreach17- understand the graph math independently from `lead-intelligence` or `connections-optimizer`18 19## When To Use This Standalone20 21Choose this skill when the user primarily wants the ranking engine:22 23- "who in my network is best positioned to introduce me?"24- "rank my mutuals by who can get me to these people"25- "map my graph against this ICP"26- "show me the bridge math"27 28Do not use this by itself when the user really wants:29 30- full lead generation and outbound sequencing -> use `lead-intelligence`31- pruning, rebalancing, and growing the network -> use `connections-optimizer`32 33## Inputs34 35Collect or infer:36 37- target people, companies, or ICP definition38- the user's current graph on X, LinkedIn, or both39- weighting priorities such as role, industry, geography, and responsiveness40- traversal depth and decay tolerance41 42## Core Model43 44Given:45 46- `T` = weighted target set47- `M` = your current mutuals / direct connections48- `d(m, t)` = shortest hop distance from mutual `m` to target `t`49- `w(t)` = target weight from signal scoring50 51Base bridge score:52 53```text54B(m) = Σ_{t ∈ T} w(t) · λ^(d(m,t) - 1)55```56 57Where:58 59- `λ` is the decay factor, usually `0.5`60- a direct path contributes full value61- each extra hop halves the contribution62 63Second-order expansion:64 65```text66B_ext(m) = B(m) + α · Σ_{m' ∈ N(m) \\ M} Σ_{t ∈ T} w(t) · λ^(d(m',t))67```68 69Where:70 71- `N(m) \\ M` is the set of people the mutual knows that you do not72- `α` discounts second-order reach, usually `0.3`73 74Response-adjusted final ranking:75 76```text77R(m) = B_ext(m) · (1 + β · engagement(m))78```79 80Where:81 82- `engagement(m)` is normalized responsiveness or relationship strength83- `β` is the engagement bonus, usually `0.2`84 85Interpretation:86 87- Tier 1: high `R(m)` and direct bridge paths -> warm intro asks88- Tier 2: medium `R(m)` and one-hop bridge paths -> conditional intro asks89- Tier 3: low `R(m)` or no viable bridge -> direct outreach or follow-gap fill90 91## Scoring Signals92 93Weight targets before graph traversal with whatever matters for the current priority set:94 95- role or title alignment96- company or industry fit97- current activity and recency98- geographic relevance99- influence or reach100- likelihood of response101 102Weight mutuals after traversal with:103 104- number of weighted paths into the target set105- directness of those paths106- responsiveness or prior interaction history107- contextual fit for making the intro108 109## Workflow110 1111. Build the weighted target set.1122. Pull the user's graph from X, LinkedIn, or both.1133. Compute direct bridge scores.1144. Expand second-order candidates for the highest-value mutuals.1155. Rank by `R(m)`.1166. Return:117   - best warm intro asks118   - conditional bridge paths119   - graph gaps where no warm path exists120 121## Output Shape122 123```text124SOCIAL GRAPH RANKING125====================126 127Priority Set:128Platforms:129Decay Model:130 131Top Bridges132- mutual / connection133  base_score:134  extended_score:135  best_targets:136  path_summary:137  recommended_action:138 139Conditional Paths140- mutual / connection141  reason:142  extra hop cost:143 144No Warm Path145- target146  recommendation: direct outreach / fill graph gap147```148 149## Related Skills150 151- `lead-intelligence` uses this ranking model inside the broader target-discovery and outreach pipeline152- `connections-optimizer` uses the same bridge logic when deciding who to keep, prune, or add153- `brand-voice` should run before drafting any intro request or direct outreach154- `x-api` provides X graph access and optional execution paths